The Adapter 's Words
Preface
About the Author
The Companion Website
To the Student
List of Symbols
1 The Foundations: Logic and Proofs
1.1 Propositional Logic
1.2 Applications of Propositional Logic
1.3 Propositional Equivalences
1.4 Predicates and Quantifiers
1.5 Nested Quantifiers
1.6 Rules of Inference
1.7 Introduction to Proofs
1.8 Proof Methods and Strategy
End-of-Chapter Material
2 Basic Structures: Sets, Functions, Sequences, Sums, and Matrices
2.1 Sets
2.2 Set Operations
2.3 Functions
2.4 Sequences and Summations
2.5 Cardinality of Sets
2.6 Matrices
End-of-Chapter Material
3 Counting
3.1 The Basics of Counting
3.2 The Pigeonhole Principle
3.3 Permutations and Combinations
3.4 Binomial Coefficients and Identities
3.5 Generalized Permutations and Combinations
3.6 Generating ermutations and Combinations
End-of-Chapter Material
4 Advanced Counting Techniques
4.1 Applications of Recurrence Relations
4.2 Solving Linear Recurrence Relations
4.3 Divide-and-Conquer Algorithms and Recurrence Relations
4.4 Generating Functions
4.5 Inclusion朎xclusion
4.6 Applications of Inclusion朎xclusion
End-of-Chapter Material
5 Relations
5.1 Relations and Their Properties
5.2 n-ary Relations and Their Applications
5.3 Representing Relations
5.4 Closures of Relations
5.5 Equivalence Relations
5.6 Partial Orderings
End-of-Chapter Material
6 Graphs
6.1 Graphs and Graph Models
6.2 Graph Terminology and Special Types of Graphs
6.3 Representing Graphs and Graph Isomorphism
6.4 Connectivity
6.5 Euler and Hamilton Paths
6.6 Shortest-Path Problems
6.7 Planar Graphs
6.8 Graph Coloring
End-of-Chapter Material
7 Trees
7.1 Introduction to Trees
7.2 Applications of Trees
7.3 Tree Traversal
7.4 Spanning Trees
7.5 Minimum Spanning Trees
End-of-Chapter Material
8 Boolean Algebra
8.1 Boolean Functions
8.2 Representing Boolean Functions
8.3 Logic Gates
8.4 Minimization of Circuits
End-of-Chapter Material
Suggested Readings
Answers to Exercises
